This paper describes the process of attaining insight in the domain of a particular insight problem--the Mutilated Checkerboard (MC) problem. Specifically, it shows that the process of attaining insight can be viewed as search, and that performance on insight problems can be predicted by the availability of sources of search constraint. To test these claims we conducted an experiment that varied the salience of features leading to the critical concept of parity in the MC problem. Using chronometric measures, analyses of verbal protocols, and computer simulation techniques, we explored first the reason for the difficulty of the Checkerboard problem, and then four potential sources of search constraint. Results concerning the effects of cue salience manipulations, prior knowledge, hints, and use of heuristics are presented. While subjects used each of these four sources of constraint, noticing properties of the situation that remained invariant during solution attempts (the Notice Invariants heuristic) was a very powerful means for focusing search for a viable problem space. We show that, in conjunction with hints and independently, it played a major part in producing insight into the solution. Keywords: Insight, Problem solving, Heuristic search.